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How do you solve #abs(x)<15#?

Answer 1

To solve the inequality \( |x| < 15 \), we consider two cases: 1. If \( x \) is positive or zero, then \( |x| = x \). 2. If \( x \) is negative, then \( |x| = -x \). For the case where \( x \) is positive or zero, the inequality becomes \( x < 15 \). For the case where \( x \) is negative, the inequality becomes \( -x < 15 \), which can be rewritten as \( x > -15 \). Therefore, the solutions to the inequality \( |x| < 15 \) are all real numbers \( x \) such that \( -15 < x < 15 \).

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Answer 2

Avery Alexander

#-15 < x < 15#

The absolute value means that the number is always positive so, for example

#|-3|=3#

So if #|x|# needs to be smaller than #15#, you can't go lower than #-15# because that would be

#|-15| = 15#

just as #|-16|# wouldn't be smaller than #15#, since it's the same as #16#. You can't go higher than #15# either because

#|15| = 15#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #abs(x)&lt;15#?

How do you solve #abs(x)<15#?